UCARE: Undergraduate Creative Activities & Research Experiences

 

Date of this Version

Spring 5-10-2020

Document Type

Poster

Citation

Poster presentation, UCARE Research Fair, Spring 2020, University of Nebraska-Lincoln.

Comments

Copyright 2020 by the authors.

Abstract

In recent years nonlocal models have been successfully introduced in a variety of applications, such as dynamic fracture, nonlocal diffusion, flocking, and image processing. Thus, the development of a nonlocal calculus theory, together with the study of nonlocal operators has become the focus of many theoretical investigations. Our work focuses on a Helmholtz decomposition in the nonlocal (integral) framework. In the classical (differential) setting the Helmholtz decomposition states that we can decompose a three dimensional vector field as a sum of an irrotational function and a solenoidal function. We will define new nonlocal gradient and curl operators that allow us to create a similar nonlocal decomposition.

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